The Slide Rules (Help me *tears*)

Two hockey pucks, labeled A and B, are initially at rest on a smooth ice surface and are separated by a distance of 18.0 . Simultaneously, each puck is given a quick push and they begin to slide directly toward each other. Puck A moves with a speed of = 2.70 , and puck B moves with a speed of = 5.10 .

What is the distance covered by puck A by the time the two pucks collide?

Really I just need to know how to set it up becuase each time I do this problem I get a negative answer when finding time and well time can't be negative can it?

The approach is perfect. You are using the equations of kinematics under a null force with puck A at the origin and puck B at x=18.0. However, the general equation of kinematics (i.e. the "model" applicable for any more under a null force) is

[tex]x(t)=x_0+v_0t[/tex]

But you have been using the (wrong) equation [tex]x(t)=x_0-v_0t[/tex] for particle B. This is where your error comes from.